Name
Title | ||
|---|---|---|
Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves |
Abstract | ||
|---|---|---|
The scalar-vector representation is used to derive a simple algorithm to obtain the roots of a quadratic quaternion polynomial. Apart from the familiar vector dot and cross products, this algorithm requires only the determination of the unique positive real root of a cubic equation, and special cases (e.g., double roots) are easily identified through the satisfaction of algebraic constraints on the scalar/vector parts of the coefficients. The algorithm is illustrated by computed examples, and used to analyze the root structure of quadratic quaternion polynomials that generate quintic curves with rational rotation-minimizing frames (RRMF curves). The degenerate (i.e., linear or planar) quintic RRMF curves correspond to the case of a double root. For polynomials with distinct roots, generating non-planar RRMF curves, the cubic always factors into linear and quadratic terms, and a closed-form expression for the quaternion roots in terms of a real variable, a unit vector, a uniform scale factor, and a real parameter @t@?[-1,+1] is derived. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jsc.2013.07.001 | J. Symb. Comput. |
Keywords | DocType | Volume |
quadratic term,distinct root,familiar vector,non-planar RRMF curve,quintic rational rotation-minimizing frame,RRMF curve,real parameter,Scalar-vector algorithm,real variable,quadratic quaternion polynomial,double root,quaternion root | Journal | 58, |
ISSN | Citations | PageRank |
0747-7171 | 2 | 0.38 |
References | Authors | |
10 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rida T. Farouki | 1 | 1396 | 137.40 |
| Petroula Dospra | 2 | 9 | 0.85 |
| Takis Sakkalis | 3 | 347 | 34.52 |